Algebra Basics: Laws Of Exponents – Math Antics
Algebra Basics: Laws Of Exponents – Math Antics

Published byRandolf Wilkins Modified over 7 years ago

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ALGEBRA 1 Lesson 1-2 Warm-Up

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ALGEBRA 1 “Exponents and Order of Operations” (1-2) What does “simplify” mean? What is a a “base” number, “exponent”, and “power”? Why is there a certain order to simplifying expressions with multiple (more than one) operations (like +, -, x, ÷ ) simplify: to make as simple as possible (in other words, what’s the answer) exponent: a shorthand way to show repeated multiplication of a base number by showing how many times to multiply the base number by itself using a superscript (a little number at the top right of the base number) power: includes both the base number and the exponent (For example, you read 5 4 as “five to the fourth power” and 5 7 as “five to the seventh power”. Exponents of 2 and 3 have special names – “squared” and “cubed”. For example, 5 2 is read as “five squared” and 5 3 is read as“five cubed There is an order of operations, because if you simplify an expression in any order you want, you’ll come up with different answers. Example:

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ALGEBRA 1 “Exponents and Order of Operations” (1-2) What is the correct order of operations? Rule: To remember the order of operations mathemeticians have agreed upon, remember PEMDAS or “Please Excuse My Dear Aunt Sally” 1.Parenthesis: Do operations within parenthesis () first. If there are parenthesis with parenthesis, such as [()] or {[()]}, work from the inside parenthesis to the outside parenthesis. 2. Exponent: Powers 3. Multiplication and Division from left to right. 4. Addition and Subtraction from left to right. Fractions: Fraction bars act as grouping symbols. For expressions like, do the calculations above and below the fraction bar before simplifying the fraction itself. Substitution: Always substitute (replace letters with numbers if you know them) before using PEMDAS.

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ALGEBRA 1 Simplify 32 + 6 2 – 14 3. 32 + 6 2 – 14 3 = 32 + 36 – 14 3 Exponent: 6 2 = 6 6 = 36. = 32 + 36 – 42Multiply 14 and 3. = 68 – 42 Add and Subtract in order from left to right. = 26 Exponents and Order of Operations LESSON 1-2 Additional Examples

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ALGEBRA 1 Evaluate 5x + 3 2 ÷ p for x = 2 and p = 3. 5x + 3 2 ÷ p = 5 2 + 3 2 ÷ 3Substitute 2 for x and 3 for p. = 5 2 + 9 ÷ 3Exponent (Power). = 10 + 3Multiply and Divide from left to right. = 13Add and Subtract from left to right. Exponents and Order of Operations LESSON 1-2 Additional Examples

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ALGEBRA 1 Find the total cost of a pair of jeans if the price is \$32 and the sales tax rate is 8%. total cost original price sales tax C=p+r p sales tax rate (in fraction or decimal form) C = p + r p = 32 + 0.08 32 Substitute 32 for p. Change 8% to 0.08 and substitute 0.08 for r. = 32 + 2.56Multiply. = 34.56Add. The total cost of the jeans is \$34.56. Exponents and Order of Operations LESSON 1-2 Additional Examples

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ALGEBRA 1 Simplify 3(8 + 6) ÷ (4 2 – 10). 3(8 + 6) ÷ (4 2 – 10) = 3(8 + 6) ÷ (16 – 10) Parenthesis (Exponent) = 3 (14) ÷ 6Parenthesis. = 42 ÷ 6Multiply and Divide from left to right. = 7Multiply and Divide from left to right. Exponents and Order of Operations LESSON 1-2 Additional Examples

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ALGEBRA 1 Evaluate each expression for x = 11 and z = 16. a. (xz) 2 = (176) 2 Parenthesis = 11 256 = 2,816 = 30,976Exponent. (xz) 2 = (11 16) 2 Substitute 11 for x and 16 for z. xz 2 = 11 16 2 b. xz 2 Exponents and Order of Operations LESSON 1-2 Additional Examples Exponent. Multiply

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ALGEBRA 1 Simplify 4[(2 9) + (15 ÷ 3) 2 ]. = 4 [ 18 + (5) 2 ]Inside Parenthesis () = 4 [18 + 25] Outside Parenthesis called brackets [Exponent] = 4 [43] Outside Parenthesis [Add] = 172 Multiply. Exponents and Order of Operations LESSON 1-2 Additional Examples

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ALGEBRA 1 A carpenter wants to build three decks in the shape of regular hexagons. The perimeter p of each deck will be 60 ft. The perpendicular distance a from the center of each deck to one of the sides will be 8.7 ft. Use the formula A = 3 ( ) to find the total area of all three decks. = 3(261)Simplify the fraction. = 783Multiply. The total area of all three decks is 783 ft 2. A = 3 ( ) pa 2 = 3 ( ) 60 8.7 2 Substitute 60 for p and 8.7 for a. = 3 ( ) 522 2 Simplify the numerator. pa 2 Exponents and Order of Operations LESSON 1-2 Additional Examples

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ALGEBRA 1 Simplify each expression. 1. 50 – 4 3 + 6 2. 3(6 + 2 2 ) – 5 3. 2[(1 + 5) 2 – (18 ÷ 3)] Evaluate each expression. 4. 4x + 3y for x = 2 and y = 4 5. 2 p 2 + 3s for p = 3 and s = 11 6. xy 2 + z for x = 3, y = 6 and z = 4 44 25 60 20 51 112 Exponents and Order of Operations LESSON 1-2 Lesson Quiz

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